Annulus Area

This is a birthday card bearing an enticing geometric gem.

It depicts two concentric circles and asks us to find the area of the annulus between them. To allow us to do that all it gives us is the length of the line AB.

Seriously? Is that enough?

After we’ve found the solution, there’s a nice Desmos animation that reveals the structure of the problem.

We assume that this is a grade 10 class that has some Desmos experience. In fact we feel that a good grade 9 class could handle this.